Four spoons of sugar (m=0.050kg, specific heat c = 1.2 kJ/kgC) at T = 20 C is ad

Question

Four spoons of sugar (m=0.050kg, specific heat c = 1.2 kJ/kgC) at T = 20 C is added to one cup of hot milk (m=0.15 kg, specific heat c = 4.0 kJ/kgC) at T = 80 C and mixed. Hint: Heat given up by milk is equal to heat gained by the sugar. Assume change of internal energy equal to (m times c times delta ?), and neglect heat loss to atmosphere and the cup, and no other heat or work interaction is taking place. Write the expression for heat loss by the milk. Write the expression for heat gain by the sugar. Calculate the final temperature of the sweetened milk. Calculate delta ? of the sugar and delta ? of the milk. Be sure assign a proper sign (positive or negative) to temperature change.

Explanation / Answer

a) Let T be the final temperature

Heat lost by milk = m*c*(80-T)

= 0.15*4*(80 - T)

b) Heat gaind by sugar = m*C*(T - 20 )

= 0.05*1.2*(T - 20)

c)  0.15*4*(80 - T) =  0.05*1.2*(T - 20)

T = (0.15*4*80 + 0.05*1.2*20) / ( 0.05*1.2 + 0.15*4 )

T = 74.55 C

Final temperature =74.55 C

d) Delta T of sugar = 74.55 - 20 = 54.55 C

Delta T of milk = 74.55 - 80 = -5.45 C

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